





import unittest

import numpy as np




def     A_      (	lowercase_   ,		lowercase_   ,		lowercase_   ,		lowercase_ = None   ,		)      ->    np.ndarray:
       _snake_case   :				List[Any]  					=    np.shape(UpperCamelCase_	)
       _snake_case   :				str  					=    np.shape(UpperCamelCase_	)
       _snake_case   :				List[str]  					=    np.shape(UpperCamelCase_	)

       if shape_a[0] != shape_b[0]:
              _snake_case   :				str  					=    (
                  '''Expected the same number of rows for A and B. '''
                  f'''Instead found A of size {shape_a} and B of size {shape_b}'''
              )
              raise ValueError(UpperCamelCase_	)

       if shape_b[1] != shape_c[1]:
              _snake_case   :				Optional[int]  					=    (
                  '''Expected the same number of columns for B and C. '''
                  f'''Instead found B of size {shape_b} and C of size {shape_c}'''
              )
              raise ValueError(UpperCamelCase_	)

       _snake_case   :				Union[str, Any]  					=    pseudo_inv
       if a_inv is None:
              try:
                     _snake_case   :				str  					=    np.linalg.inv(UpperCamelCase_	)
              except np.linalg.LinAlgError:
                     raise ValueError(
                         '''Input matrix A is not invertible. Cannot compute Schur complement.'''	)

       return mat_c - mat_b.T @ a_inv @ mat_b

class 					A     (unittest.TestCase					):



      def  __a			(       self       )   -> None:



             '''simple docstring'''

             _snake_case   :				int  					=    np.array([[1, 2, 1], [2, 1, 2], [3, 2, 4]]       )
             _snake_case   :				Dict  					=    np.array([[0, 3], [3, 0], [2, 3]]       )
             _snake_case   :				int  					=    np.array([[2, 1], [6, 3]]       )

             _snake_case   :				List[str]  					=    schur_complement(_UpperCAmelCase  ,	_UpperCAmelCase  ,	_UpperCAmelCase       )

             _snake_case   :				List[Any]  					=    np.block([[a, b], [b.T, c]]       )

             _snake_case   :				Tuple  					=    np.linalg.det(_UpperCAmelCase       )
             _snake_case   :				Union[str, Any]  					=    np.linalg.det(_UpperCAmelCase       )
             _snake_case   :				str  					=    np.linalg.det(_UpperCAmelCase       )

             self.assertAlmostEqual(_UpperCAmelCase  ,	det_a * det_s       )



      def  __a			(       self       )   -> None:



             '''simple docstring'''

             _snake_case   :				List[Any]  					=    np.array([[1, 2, 1], [2, 1, 2], [3, 2, 4]]       )
             _snake_case   :				List[str]  					=    np.array([[0, 3], [3, 0], [2, 3]]       )
             _snake_case   :				Dict  					=    np.array([[2, 1], [6, 3]]       )

             with self.assertRaises(_UpperCAmelCase       ):
                    schur_complement(_UpperCAmelCase  ,	_UpperCAmelCase  ,	_UpperCAmelCase       )



      def  __a			(       self       )   -> None:



             '''simple docstring'''

             _snake_case   :				Optional[int]  					=    np.array([[1, 2, 1], [2, 1, 2], [3, 2, 4]]       )
             _snake_case   :				Any  					=    np.array([[0, 3], [3, 0], [2, 3]]       )
             _snake_case   :				int  					=    np.array([[2, 1, 3], [6, 3, 5]]       )

             with self.assertRaises(_UpperCAmelCase       ):
                    schur_complement(_UpperCAmelCase  ,	_UpperCAmelCase  ,	_UpperCAmelCase       )


if __name__ == "__main__":
   import doctest

   doctest.testmod()
   unittest.main()











'''simple docstring'''

from typing import TYPE_CHECKING

from ....utils import OptionalDependencyNotAvailable, _LazyModule, is_torch_available, is_vision_available


SCREAMING_SNAKE_CASE__     :						Tuple	=  {'''configuration_van''': ['''VAN_PRETRAINED_CONFIG_ARCHIVE_MAP''', '''VanConfig''']}


try:
			if not is_torch_available():
						raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
			pass
else:
			SCREAMING_SNAKE_CASE__     :						List[str]	=  [
			    '''VAN_PRETRAINED_MODEL_ARCHIVE_LIST''',
			    '''VanForImageClassification''',
			    '''VanModel''',
			    '''VanPreTrainedModel''',
			]

if TYPE_CHECKING:
			from .configuration_van import VAN_PRETRAINED_CONFIG_ARCHIVE_MAP, VanConfig

			try:
						if not is_torch_available():
									raise OptionalDependencyNotAvailable()
			except OptionalDependencyNotAvailable:
						pass
			else:
						from .modeling_van import (
						    VAN_PRETRAINED_MODEL_ARCHIVE_LIST,
						    VanForImageClassification,
						    VanModel,
						    VanPreTrainedModel,
						)

else:
			import sys

			SCREAMING_SNAKE_CASE__     :						Dict	=  _LazyModule(__name__, globals()['''__file__'''], _import_structure)




